Find the velocity of image,when object and mirror both are moving towards each other with velocities `4ms^(-1) and 5ms^(-1)` respectively, is

Options

A. `-14ms^(-1)`
B. `15ms^(-1)`
C. `-9ms^(-1)`
D. `14ms^(-1)`

Explanation

To find the velocity of the image when both the object and the mirror are moving towards each other, we can follow these steps:

### Step 1: Define the velocities
Let:
- Velocity of the object (Vo) = 4 m/s (towards the mirror)
- Velocity of the mirror (Vm) = 5 m/s (towards the object)

### Step 2: Establish the direction
Assume the direction towards the mirror is positive. Therefore:
- Vo = +4 m/s
- Vm = +5 m/s

### Step 3: Use the formula for velocity of the image
In the case of a plane mirror, the velocity of the image (Vi) relative to the mirror can be calculated using the formula:
\[ Vi = -Vo + 2Vm \]
This formula accounts for the fact that the image moves in the opposite direction to the object and is affected by the motion of the mirror.

### Step 4: Substitute the values
Substituting the values into the formula:
\[ Vi = -4 + 2(5) \]
\[ Vi = -4 + 10 \]
\[ Vi = 6 \text{ m/s} \]

### Step 5: Determine the direction of the image's velocity
Since the image's velocity is positive, it indicates that the image is moving in the same direction as the mirror. However, since the object and mirror are moving towards each other, we can conclude that the image is moving away from the object.

### Final Result
The velocity of the image is:
\[ Vi = 6 \text{ m/s} \]